Banks should provide in-branch internet access so people without access to the web do not miss out on the best deals, according to the Consumer Association.
The study by Which? found that an online banking customers could be 37% better off over a year, saving up to £375, compared with a branch-only user.
The average rate for instant access savings accounts available in branch is 0.56%, half of that available to online savers, while fixed-rate savings accounts, current accounts and cash ISAs also offer better rates for online savers, the report found.
"Banks should be more inclusive by offering terminals in branches where customers could access online deals, with some help from staff," said chief executive of Which?, Peter Vicary-Smith.
The difference represented a cost saving which the banks were passing on to customers, said Brian Capon, assistant director of the British Bankers' Association. "Banks provide a range of products for different needs and, like any other businesses, they have to look at the relative costs. As it's less costly to deliver via the internet than through the branch, there's often a difference in price," he added.
But Michelle Mitchell, director of charity Age UK, said older people are being hit the hardest.
"While more should be done to help older people get online if they want to, banks should also ensure that their financial products are more inclusive," said Michelle Mitchell.
However, the most recent financial institution to open on the high street, Metro Bank, still requires customers to physically enter the branch to open accounts.